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   <div id="projectname">Parallel Gaussian Process Regression
   &#160;<span id="projectnumber">1.0.0</span>
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   <div id="projectbrief">The implementation of parallel Gaussian process (GP) regression is based on the following publication: Jie Chen, Nannan Cao, Kian Hsiang Low, Ruofei Ouyang, Colin Keng-Yan Tan &amp; Patrick Jaillet. Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations. In Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence (UAI 2013), Bellevue, WA, Jul 11-15, 2013.</div>
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<div class="title">pgpr_chol.h</div>  </div>
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<a href="pgpr__chol_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;</div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="preprocessor">#ifndef _PGPR_CHOL_H_</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="preprocessor">#define _PGPR_CHOL_H_</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="pgpr__type_8h.html">pgpr_type.h</a>&quot;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"><a class="line" href="classpgpr__chol.html">   14</a></span>&#160;<span class="keyword">class </span><a class="code" href="classpgpr__chol.html">pgpr_chol</a></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;{</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;    Int n;   </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;    <a class="code" href="classpgpr__matrix.html">Mdoub</a> el;  </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;    <a class="code" href="classpgpr__matrix.html">Mdoub</a> elt;  </div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00028"></a><span class="lineno"><a class="line" href="classpgpr__chol.html#ade89a39def082f6de79df242a39fad67">   28</a></span>&#160;  <a class="code" href="classpgpr__chol.html#ade89a39def082f6de79df242a39fad67">pgpr_chol</a>(<a class="code" href="classpgpr__matrix.html">Mdoub</a> &amp;A) :  el(A), elt(A) {</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    Int i, j, k;</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <a class="code" href="classpgpr__vector.html">Vdoub</a> tmp;</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    Doub sum;</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;        n = A.nrows();</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="keywordflow">if</span> (el.ncols() != n) <span class="keywordflow">throw</span>(<span class="stringliteral">&quot;need square matrix&quot;</span>);</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;      <span class="keywordflow">for</span> (j = i; j &lt; n; j++) {</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;        <span class="keywordflow">for</span> (sum = el[i][j], k = i - 1; k &gt;= 0; k--) sum -= el[i][k] * el[j][k];</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;        <span class="keywordflow">if</span> (i == j) {</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;          <span class="keywordflow">if</span> (sum &lt;= 0.0)</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;            <span class="keywordflow">throw</span>(<span class="stringliteral">&quot;pgpr_chol failed&quot;</span>);</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;          el[i][i] = sqrt(sum);</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;        } <span class="keywordflow">else</span> el[j][i] = sum / el[i][i];</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;      }</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    }</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) <span class="keywordflow">for</span> (j = 0; j &lt; i; j++) el[j][i] = 0.;</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) <span class="keywordflow">for</span> (j = 0; j &lt; n; j++) elt[j][i] = el[i][j];</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;  }</div>
<div class="line"><a name="l00052"></a><span class="lineno"><a class="line" href="classpgpr__chol.html#a567b23e2e93a85675de26550d5e4cb38">   52</a></span>&#160;  <span class="keywordtype">void</span> <a class="code" href="classpgpr__chol.html#a567b23e2e93a85675de26550d5e4cb38">solve</a>(<a class="code" href="classpgpr__vector.html">Vdoub</a> &amp;b, <a class="code" href="classpgpr__vector.html">Vdoub</a> &amp;x) {</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    Int i, k;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    Doub sum;</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keywordflow">if</span> (b.size() != n || x.size() != n) <span class="keywordflow">throw</span>(<span class="stringliteral">&quot;bad lengths in pgpr_chol&quot;</span>);</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;      <span class="keywordflow">for</span> (sum = b[i], k = i - 1; k &gt;= 0; k--) sum -= el[i][k] * x[k];</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;      x[i] = sum / el[i][i];</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    }</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="keywordflow">for</span> (i = n - 1; i &gt;= 0; i--) {</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;      <span class="keywordflow">for</span> (sum = x[i], k = i + 1; k &lt; n; k++) sum -= elt[i][k] * x[k];</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;      x[i] = sum / el[i][i];</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    }</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  }</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;  <span class="keywordtype">void</span> elmult(<a class="code" href="classpgpr__vector.html">Vdoub</a> &amp;y, <a class="code" href="classpgpr__vector.html">Vdoub</a> &amp;b) {</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    Int i, j;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    <span class="keywordflow">if</span> (b.size() != n || y.size() != n) <span class="keywordflow">throw</span>(<span class="stringliteral">&quot;bad lengths&quot;</span>);</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;      b[i] = 0.;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;      <span class="keywordflow">for</span> (j = 0; j &lt;= i; j++) b[i] += el[i][j] * y[j];</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    }</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;  }</div>
<div class="line"><a name="l00078"></a><span class="lineno"><a class="line" href="classpgpr__chol.html#a365839254c16b047b2e36a7937b8593f">   78</a></span>&#160;  <span class="keywordtype">void</span> <a class="code" href="classpgpr__chol.html#a365839254c16b047b2e36a7937b8593f">elsolve</a>(<a class="code" href="classpgpr__vector.html">Vdoub</a> &amp;b, <a class="code" href="classpgpr__vector.html">Vdoub</a> &amp;y) {</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    Int i, j;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    Doub sum;</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    <span class="keywordflow">if</span> (b.size() != n || y.size() != n) <span class="keywordflow">throw</span>(<span class="stringliteral">&quot;bad lengths&quot;</span>);</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;      <span class="keywordflow">for</span> (sum = b[i], j = 0; j &lt; i; j++) sum -= el[i][j] * y[j];</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;      y[i] = sum / el[i][i];</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    }</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  }</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;</div>
<div class="line"><a name="l00090"></a><span class="lineno"><a class="line" href="classpgpr__chol.html#a8da419135a59362c31674091b0bfcf89">   90</a></span>&#160;  <span class="keywordtype">void</span> <a class="code" href="classpgpr__chol.html#a8da419135a59362c31674091b0bfcf89">inverse</a>(<a class="code" href="classpgpr__matrix.html">Mdoub</a> &amp;ainv) {</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    Int i, j, k;</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    Doub sum;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    ainv.resize(n, n);</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) <span class="keywordflow">for</span> (j = 0; j &lt;= i; j++) {</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;        sum = (i == j ? 1. : 0.);</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;        <span class="keywordflow">for</span> (k = i - 1; k &gt;= j; k--) sum -= el[i][k] * ainv[j][k];</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        ainv[j][i] = sum / el[i][i];</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;      }</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    <span class="keywordflow">for</span> (i = n - 1; i &gt;= 0; i--) <span class="keywordflow">for</span> (j = 0; j &lt;= i; j++) {</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;        sum = (i &lt; j ? 0. : ainv[j][i]);</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;        <span class="keywordflow">for</span> (k = i + 1; k &lt; n; k++) sum -= elt[i][k] * ainv[j][k];</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        ainv[i][j] = ainv[j][i] = sum / el[i][i];</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;      }</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;  }</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;</div>
<div class="line"><a name="l00108"></a><span class="lineno"><a class="line" href="classpgpr__chol.html#a72827b33f276569fa6c3c8f2af80c40e">  108</a></span>&#160;  Doub <a class="code" href="classpgpr__chol.html#a72827b33f276569fa6c3c8f2af80c40e">logdet</a>() {</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    Doub sum = 0.;</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    <span class="keywordflow">for</span> (Int i = 0; i &lt; n; i++) sum += log(el[i][i]);</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <span class="keywordflow">return</span> 2.*sum;</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  }</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;};</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="ttc" id="classpgpr__chol_html_ade89a39def082f6de79df242a39fad67"><div class="ttname"><a href="classpgpr__chol.html#ade89a39def082f6de79df242a39fad67">pgpr_chol::pgpr_chol</a></div><div class="ttdeci">pgpr_chol(Mdoub &amp;A)</div><div class="ttdoc">The constructor does a Cholesky factorization. </div><div class="ttdef"><b>Definition:</b> pgpr_chol.h:28</div></div>
<div class="ttc" id="classpgpr__chol_html_a72827b33f276569fa6c3c8f2af80c40e"><div class="ttname"><a href="classpgpr__chol.html#a72827b33f276569fa6c3c8f2af80c40e">pgpr_chol::logdet</a></div><div class="ttdeci">Doub logdet()</div><div class="ttdoc">Calculate the determinant of square matrix and retrun in log scale. </div><div class="ttdef"><b>Definition:</b> pgpr_chol.h:108</div></div>
<div class="ttc" id="classpgpr__chol_html_a567b23e2e93a85675de26550d5e4cb38"><div class="ttname"><a href="classpgpr__chol.html#a567b23e2e93a85675de26550d5e4cb38">pgpr_chol::solve</a></div><div class="ttdeci">void solve(Vdoub &amp;b, Vdoub &amp;x)</div><div class="ttdoc">Solving A* x = b using back substitution. </div><div class="ttdef"><b>Definition:</b> pgpr_chol.h:52</div></div>
<div class="ttc" id="classpgpr__chol_html"><div class="ttname"><a href="classpgpr__chol.html">pgpr_chol</a></div><div class="ttdoc">This class provides Cholesky factorization and some related useful functions such as inverse...</div><div class="ttdef"><b>Definition:</b> pgpr_chol.h:14</div></div>
<div class="ttc" id="pgpr__type_8h_html"><div class="ttname"><a href="pgpr__type_8h.html">pgpr_type.h</a></div><div class="ttdoc">This file provides important macros, templates, basic data types (e.g., vector, matrix). </div></div>
<div class="ttc" id="classpgpr__vector_html"><div class="ttname"><a href="classpgpr__vector.html">pgpr_vector&lt; Doub &gt;</a></div></div>
<div class="ttc" id="classpgpr__matrix_html"><div class="ttname"><a href="classpgpr__matrix.html">pgpr_matrix&lt; Doub &gt;</a></div></div>
<div class="ttc" id="classpgpr__chol_html_a8da419135a59362c31674091b0bfcf89"><div class="ttname"><a href="classpgpr__chol.html#a8da419135a59362c31674091b0bfcf89">pgpr_chol::inverse</a></div><div class="ttdeci">void inverse(Mdoub &amp;ainv)</div><div class="ttdoc">Compute the inverse of a matrix. </div><div class="ttdef"><b>Definition:</b> pgpr_chol.h:90</div></div>
<div class="ttc" id="classpgpr__chol_html_a365839254c16b047b2e36a7937b8593f"><div class="ttname"><a href="classpgpr__chol.html#a365839254c16b047b2e36a7937b8593f">pgpr_chol::elsolve</a></div><div class="ttdeci">void elsolve(Vdoub &amp;b, Vdoub &amp;y)</div><div class="ttdoc">solving el * y = b using back substitution. </div><div class="ttdef"><b>Definition:</b> pgpr_chol.h:78</div></div>
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